How would I achieve to make a set distance from a part?

local player = game.Players.LocalPlayer
local Character = player.Character or player.CharacterAdded:Wait()
local humanoidrootpart = Character:WaitForChild("HumanoidRootPart")
local mouse = player:GetMouse()
local OFFSET = 10

mouse.Button1Up:Connect(function()
    Down = false
end)


mouse.Button1Down:Connect(function()
    local part = Instance.new("Part")
    part.Parent = workspace

    local BP = Instance.new("BodyPosition")
    BP.Parent = part
    BP.MaxForce = Vector3.new(math.huge, math.huge, math.huge)
    Down = true
    while Down == true do
        wait()
    local Direction = (mouse.Hit.p - humanoidrootpart.Position).Unit
        BP.Position = humanoidrootpart.Position + (Direction * OFFSET)
    end
end)

Let me explain the changes. Firstly, you want to create a unit length vector that points out from your character to your mouse location. That's how you can make create a position relative to your character. Secondly , if you want your part to point out 10 studs away from your character, you want to make a offset. The position of the part should be on your character (I prefer HumanoidRootPart) and then you add your offset.

Also, I want to point out that the reason that I chose to type:

local part = Instance.new("Part")
part.Parent = workspace

instead of:

local part = Instance.new("Part", workspace)

Is because it causes performance issues. You can read more about it here. Just a tip.

This is a very simple vector problem, which can be solved as follows:

First get the target position (mouse.Hit.p)

Then you calculate the unit vector from the humanoid root part to the target position

Multiply the unit vector by the distance you want the part to be

And finally, BP position = humanoid root part position + (direction * distance)

Here is the modified code:

local player = game.Players.LocalPlayer
local char = player.Character or player.CharacterAdded:wait()
local hrp = char.HumanoidRootPart
local mouse = player:GetMouse()

mouse.Button1Up:Connect(function()
    Down = false
end)


mouse.Button1Down:Connect(function()
    local part = Instance.new("Part", workspace)

    local BP = Instance.new("BodyPosition", part)
    BP.MaxForce = Vector3.new(math.huge, math.huge, math.huge)
    Down = true
    while Down == true do
        wait()
        local targetPos = mouse.Hit.p
        local direction = (targetPos - hrp.CFrame.p).Unit
        BP.Positon = hrp.CFrame.p + direction * 10
    end
end)